The present invention relates to a method of evaluating the endurance of vehicle wheel (rim) made of aluminum, steel, etc., wherein the distribution of stress applied to the wheel during the dynamic radial fatigue test is calculated by linear numerical analysis.
A testing apparatus for evaluating the dynamic radial fatigue of vehicle wheel is schematically shown in FIG. 1. In the dynamic radial fatigue test, a wheel 3 on which a tire 1 is mounted is pressed on a peripheral surface of a drum 4 rotating in the direction indicated by an arrow B. The wheel 3 and the tire 1 are allowed to rotate for a long period of time to evaluate the fatigue endurance of the wheel 3.
In the conventional methods, a physical wheel manufactured through the wheel design, the mold manufacturing and the casting has been actually subjected to the dynamic radial fatigue test to evaluate the endurance of the wheel. Since the dynamic radial fatigue test is a fatigue endurance test, the time taken to obtain results is from one to two weeks. If the results are not satisfactory, after the wheel design is changed and the mold is modified, another physical wheel should be cast and the dynamic radial fatigue test should be repeated on the wheel (FIG. 9). This requires much time and labor to prevent an expeditious development of a new wheel.
The evaluation methods by a computational simulation using numerical analysis have lately attracted considerable attention in the field of automotive parts. For example, Japanese Patent Laid-Open No. 7-164815 discloses a computational designing method of pneumatic tire by nonlinear analysis. It has been expected that the results of the dynamic radial fatigue test can be predicted and the wheel design and the mold design can be changed or modified based on the predicted results without manufacturing physical wheel or mold, thereby expediting the development of new wheels, if the computational simulation can be applied to the evaluation of dynamic radial fatigue of vehicle wheels. However, since the dynamic radial fatigue test involves the nonlinear problems of the tire structure and the contact problem between the tire and the drum, the computational analysis of the test has been presumed to require a lot of time for solving the nonlinear problems. Therefore, the computational simulation of the dynamic radial fatigue test has not yet been put to practical use.
FIG. 2 shows a finite element model which may be applicable to nonlinear numerical analysis for simulating the dynamic radial fatigue test of a wheel. As seen from FIGS. 1 and 2, the tire portion, the air pressure portion 2, the press-contacting effect of the tire bead portion 6 against the wheel flange 5 which occurs in combination with weight of the tire portion and the pressure from the air pressure portion, and the load (A in FIGS. 1 and 22 in FIG. 2) applied through the contact between the drum and the tire are directly modeled for numerical analysis in conformity with the geometric shape of the tire and wheel.
The wheel portion is modeled by three-dimensional solid elements. Since the tire portion is made of a nonlinear composite materials comprising a rubber matrix and a reinforcing filler such as steel wire and nylon cord, the tire portion is modeled as an anisotropic nonlinear material. The air pressure portion is modeled as a compressible air. The press-contact effect of the tire bead portion against the wheel flange, which is a composite action of the weight of tire portion and the air pressure, is treated as a contact problem between the tire bead portion and the tire flange as indicated by reference numeral 21 in FIG. 2. The load applied through the contact between the tire and the drum as the contacting force of the tire bead portion to the wheel flange is treated as a nonlinear contact problem between the tire and the drum as indicated by reference numeral 23 in FIG. 2.
To solve the above problems, the portions other than the wheel portion should be modeled in exact conformity with the geometric shapes. Therefore, in the above method, the tire portion should be represented by nonlinear three-dimensional solid elements and the distribution of stress is calculated by the nonlinear analysis including the analysis of a large strain and large deformation.
Thus, in the above method, various nonlinear factors such as the nonlinear tire material, the contact problem between the drum and the tire, the contact problem between the tire bead portion and the wheel flange and the compression problem of the air in the tire should be calculated simultaneously with the calculation of the stress generated on the wheel. Such a calculation takes a lot of time even when a super computer is used.
Since, in the dynamic radial fatigue test, both the wheel and the tire are rotated on the drum, the dynamic radial fatigue test is difficult to be simulated by symmetric analysis although depending on the wheel design. This prevents the dynamic radial fatigue test from being simulated by a model simplified by the symmetry of the system, although the symmetry is usually employed in various numerical analysis. Therefore, the complete system of the dynamic radial fatigue test including the wheel should be modeled. This makes the analysis time unduly long and sometimes the analysis cannot be completed due to a large number of factors to be analyzed.
As mentioned above, the method utilizing nonlinear analysis requires an expensive computer, a large storage capacity and a large memory capacity as well as a lot of time for the wheel design. Therefore, the nonlinear computational simulation method is considered to make little contribution to promoting the development of the wheel.